Reference problem
=====================


.. _Ref482175678:


Geometry
---------

The geometry is chosen deliberately simple, to translate a state of homogeneous stresses and deformations, as is the case in uniaxial traction. This is a volume element represented by a square with side :math:`\mathrm{0.01mm}`. The modeling is axisymmetric, and the traction takes place with imposed deformation.


Material properties
----------------------

The characteristics set are as follows:

Keyword ELAS:

YOUNG = :math:`143006.0\mathrm{MPa}`

NU= :math:`0.33`

UN_SUR_M = :math:`0`

G2_0= :math:`0.28`

The initial values and limits of the parameters to be identified are:


.. csv-table::

    "**Keyword** **CIN2_CHAB**", "**Initial value**", "**Inf terminal**", "**Upper terminal**"
    "R0", "100", "0.01", "1000"
    "R_I", "120", "0.01", "2000"
    "B", "0.0934", "0.01", "20"
    "K", "4.307", "0.01", "20"
    "W", "0.156", "0.01", "20"
    "G1_0", "245", "0.01", "2000"
    "C1_I", "2628", "0.01", "20000"
    "C2_I", "105", "0.01", "2000000"
    "A_I", "1.24", "0.01", "2000"
    "**Keyword** **LEMAITRE**", "", "", ""
    "UN_SUR_K ", "0.003", "0.00001", "2000"
    "EXP_N ", "15", "0.01", "2000"



Boundary conditions and loads
-------------------------------------

:math:`\mathrm{DY}=0` on the bottom

:math:`\mathrm{DX}=0` on the left side

:math:`\mathrm{DY}` imposed on the top, such as:

:math:`\mathrm{DY}(t)=({\mathrm{EPS}}_{\mathrm{final}}\ast H)/\mathrm{tmax}\ast t`

With :math:`{\mathrm{EPS}}_{\mathrm{final}}=0.01`

:math:`H=0.01\mathrm{mm}`

:math:`\mathrm{Tmax}=\mathrm{200s},\mathrm{1000s},\mathrm{2000s},\mathrm{10000s}`

This corresponds to imposed deformation rates of :math:`{5.10}^{-4}/s,{1.10}^{-3}/s,{5.10}^{-3}/s,{1.10}^{-6}/s`.


Initial conditions
--------------------

Zero stresses and deformations.


Reference curves
--------------------


.. image:: images/10000000000002D500000203AD62E34B57A08B6A.jpg
    :width: 6.1165in
    :height: 4.3453in


.. _RefImage_10000000000002D500000203AD62E34B57A08B6A.jpg:

The curves obtained with the initial values of the parameters are as follows:


.. image:: images/10000000000002D5000002022C90721E334E057B.jpg
    :width: 6.1165in
    :height: 4.3366in


.. _RefImage_10000000000002D5000002022C90721E334E057B.jpg: